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Page 1: Elastic Deformations for Data Augmentation in …contrast-limited adaptive histogram equalization (CLAHE) is applied. Also, image size is reduced by a factor of 12, using pixel area

Elastic Deformations for Data Augmentation in Breast Cancer MassDetection

Eduardo Castro1, Jaime S. Cardoso1,2 and Jose Costa Pereira1,3

{eduardo.m.castro , jaime.cardoso , jose.c.pereira} @inesctec.pt

Abstract— Two limitations hamper performance of deeparchitectures for classification and/or detection in medicalimaging: (i) the small amount of available data, and (ii) theclass imbalance scenario. While millions of labeled images areavailable today to build classification tools for natural scenes,the amount of available annotated data for automatic breastcancer screening is limited to a few thousand images, at best. Weaddress these limitations with a method for data augmentation,based on the introduction of random elastic deformations onimages of mammograms. We validate this method on threepublicly available datasets.

Our proposed Convolutional Neural Network (CNN) archi-tecture is trained for mass classification – in a conventionalway –, and then used in the more interesting problem of massdetection in full mammograms by transforming the CNN intoa Fully Convolutional Network (FCN).

I. INTRODUCTION

Worldwide, breast cancer is the most lethal form of cancerin women [1]. It is estimated that 1.7 million new cases and520 thousand deaths happen due to it every year; makingit one of the biggest health concerns in modern society.Similar to other forms of cancer, early detection is criticalfor successful treatment. The National Cancer Institute (NCI)states that when diagnosed in early stages, survival ratesare nearly 100%, unfortunately dropping to 22% for laterdiagnosis [2]. One difficulty for early diagnosis arises fromthe fact that, initially, breast cancer is asymptomatic. As such,detection needs to be done through screening.

In mammograms, radiologists look for malignant lesions– often subtle – with an eye for detail. The screening ofa large group of women substantially increases specializedworkload. This is aggravated in double reading scenarios,which have been shown to yield better detection rates [3].With this problem in mind, many algorithms have beenproposed by the scientific community to assist radiologistsduring diagnosis, increasing early detection rates while alsoreducing workload [4]. These Computer Aided Detectionsystems traditionally work by first detecting, segmenting andcharacterizing lesions using heuristic algorithms and thenclassifying them using machine learning [5].

For detection and segmentation, approaches are oftenbased on the bright appearence of masses [6] or by detectingobject edges on the mammogram [7], [8]. Characterization isusually done with a wide set of features related to intensity,

1INESCTEC, Porto 4200-465, Portugal2Department of Electrical and Computer Engineering, School of Engi-

neering, Porto University, Porto 4200-465, Portugal3Department of Computer Science, School of Engineering, Porto Uni-

versity, Porto 4200-465, Portugal

morphology and generic texture descriptors [9]. For theclassification task, Support Vector Machines and RandomForests are still widely used, but other classification toolscan be found [10].

The recent success of deep learning architectures in manyvisual recognition tasks [11] has motivated researchers to fa-vor these methods instead of the traditional CAD pipeline formammogram screening [9], [12]. These architectures includefeature learning and classification in a single framework, andthey can easily be adapted to perform detection and seg-mentation. Rather than using heuristics, these architectureswork by minimizing a certain loss function that encodes theclassification error from a set of labeled samples.

In breast cancer detection, as in other medical imagingapplications, the number of healthy samples largely exceedsthat of unhealthy ones. If care is not taken this will lead tobiased models. Additionally, the cost of missing a malignantmass is much higher than a false detection (predicting malig-nant when in fact it’s benign, or no mass exists). Due to this,CAD platforms tend to favor high sensitivity at the expense ofmore false positives per image. On the other hand, it is wellestablished that deep learning models require a high numberof labeled examples. Otherwise they tend to under-performtraditional classification methods. The relatively small size ofmammogram datasets (particularly in unhealthy cases) andthe general scarcity of labeled data in this area, makes it hardto train good deep learning models for mass detection.

To counter the effect of the small number of availablesamples, data augmentation techniques (e.g. rotations, scalingor translations) are often used. In this work, we explore a newtechnique of elastic distortions. The rationale of using thistype of data augmentation is as follows. Because the breastis a non-rigid object which is stretched before the X-ray, thesame breast can appear with slightly different appearancein different exams due to different stretching. As such, onecan artificially introduce similar small elastic distortions tocreate new artificial samples that are physically plausible. Wealso propose a new Convolutional Neural Network (CNN)topology to show that elastic distortions on mammogramscan significantly improve mass detection performance onCAD systems.

Our contributions in this manuscript are thus two-folded:(i) a new architecture for mass classification inspired in theVGG model of [13], and (ii) a data augmentation strategyusing elastic deformations motivated by the nature of breastlesions, and the scarcity data for mass detection.

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II. METHODOLOGY

In this section, we describe our proposed framework formass detection. We start by an overview of the prepro-cessing and patch extraction tasks. Then, we proceed todetail the proposed network topology and the adopted dataaugmentation strategy – based on elastic deformations of themammograms. We conclude with an end-to-end overview ofthe proposed mass detection method.

Preprocessing: mammogram images are first processedto: (i) correct contrast by adaptive histogram equalization,(ii) separate the breast tissue from the background, and (iii)remove image artifacts (e.g. film boundary, watermarks). Thefirst step is used to reduce variability between images; acontrast-limited adaptive histogram equalization (CLAHE)is applied. Also, image size is reduced by a factor of 12,using pixel area relation interpolation. In this method eachpixel’s intensity in the down-sampled image is set to themean of the corresponding region in the original image.Resizing allows the overwhelming majority of lesions tofit an input of size of (76 × 76), dramatically reducing therequired computational power. Finally pixel intensity range iscentered around zero by remapping intensities linearly to therange [−0.5, 0.5] which provides numerical stability duringtraining [14]. Second, the image region containing tissue(ROI) is separated from the background using morphologicalfiltering, image subtraction and thresholding; similar to [15].Additionally, we only keep the binary object with the largestarea and perform a dilation to guaranty the whole breast isinside the ROI. Pixels in the mammogram outside this regionare set to zero, which eliminates most of the digitizationartifacts.

Patch extraction: traditional data augmentation involvesrotations, mirroring and translations. For rotation and mir-roring, parameters are an angle in the range [0, 2π[ and aboolean value, respectively. The full image is rotated (mir-rored) and patches of fixed-size – (76× 76) – are collectedfrom the rotated (mirrored) mammogram. Translations areadded by collecting multiple nearby patches for each lesion.The full-scheme for data augmentation based on elasticdeformations of the mammogram is detailed in Section II-B.For each lesion, a total of 9 positive patches centered in thered dots are collected, see Figure 1. Negative patches arecollected by grid sampling the image with a fixed-step equalto 50% of the patch length. Their centers are represented bythe blue dots of Figure 1.

A. Convolutional Neural Networks

The neocognitron [16], proposed in the 80’s byFukushima, triggered the development of Convolutional Neu-ral Networks, a broader class of networks that have becamea mainstream tool for visual recognition tasks. They modeldata using a composition of relatively simple functions calledlayers and parameterized by weights. The same model cansolve many different tasks as long as a “good” set of weightscan be found; usually through an optimization process calledlearning.

Fig. 1: Selected points for patch extraction. Blue and reddots indicate negative and positive patch centers, respectively.Red square indicates the lesion bounding box. Green squareindicates patch size.

In this work a new architecture is proposed, inspired inthe design principles described by Simonyan and Zissermanin [13]. All filters are 3×3 and the depth varies depending onthe position of the layer within the network. Rectifier LinearUnits (ReLU) are used after each convolutional layer, whichhave been shown to decrease the overall training time, whileincreasing the network’s discriminative power [17]. Weightinitialization is done as proposed by Gorot and Bengioin [18]. For training, categorical cross-entropy is minimizedusing Adam [19], a gradient descent algorithm which in-cludes momentum and an adaptive learning rate for eachvariable. In practice these properties reduce the importanceof weight initialization and hyper-parameter optimization inthe final solution, while also allowing a faster convergence.

The ultimate goal is to obtain a probability map thatemphasizes the regions of a mammogram that are more likelyto have a lesion. We formulate this detection problem as aclassification one. First, a CNN patch classifier is trained ina conventional way. This patch classifier is then transformedinto a fully convolutional network , which classifies thewhole image in one forward pass and outputs the samenumerical result as screening with the patch classifier in asliding window fashion, while taking much less time. Thetransformation is done by operating three changes in a layer-wise fashion. (1) The input layer is made bigger to fit a wholemammogram. (2) For max-pooling layers, the (2 × 2) filteris applied to four copies of the image starting at differentpixel locations – {(0, 0); (0, 1); (1, 0); (1, 1)} (as in [20]).(3) Dense layers are implemented as convolutional ones byreshaping weights and operations (as in [21]). A schematicwith the proposed detection method is shown in Figure 2.The upper part of the diagram focuses on the patch-basedtraining architecture, while the lower half emphasizes thechanges made for inference on full mammograms.

B. Elastic Deformations

In a continuous body, a deformation results from a stressfield induced by applied forces1. If the deformation recoversafter the stress field has been removed the deformationsare called elastic. This phenomena can realistically occur in

1changes in the temperature field can also cause deformations, but theyare out of scope of the current application.

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sharedweights

Conv w/ ReLU

Max pool 2x2

Dropout (20%)

DenseMammogram

Patches

Prob. map

Training

Inference

Patch Prob.

128256

51264

(3x3) (6x6) (1x1) (1x1)

(0.2 ; 0.8)

Fig. 2: Overview of the proposed framework. Numbers on top of layers correspond to either number of filters (convolutionallayers) or neurons (dense layers). Numbers at the bottom correspond to the filter size of the convolutional layers.

breast cancer screening. For each exam, a slightly differentstretch is applied due to the position of the breast and thestrength used in the compression. As such, the same breastobserved in two different screenings may have differentappearances, which should not influence the decision ofwhether a lesion is present or not. Elastic deformations as adata augmentation technique, therefore, comes naturally as amethod to model these variations.

(a) Original (b) Deformed

Fig. 3: Effects of performing elastic deformation on a mam-mogram.

In CNNs, these transformations have been used for dataaugmentation in handwritten digit recognition tasks [22]. Tothe best of our knowledge, this is the first work that useselastic deformations to generate synthetic samples of cancermasses. Recognizing that breast tissue is not a rigid-body –and as such is subject to deformations – is a stepping stonethat makes way for alternative methods of data augmentation.The synthetic samples are used to artificially increase the dataavailable for training.

Obtaining a deformation on a mammogram image is donein two parts. First a random stress field is generated for thehorizontal and vertical directions, ∆x, and ∆y respectively.For each pixel and direction, a random value in the rangeof α × [−0.5, 0.5] is uniformly picked. To ensure closepixels have similar displacement the resulting horizontaland vertical images are applied a Gaussian filter separately(eq. (1) and (2)). These transformations have two parameters:

the maximum value for the random initial displacement (α)and the strength of the smoothing operation, given by thestandard deviation of the Gaussian filter (σ). We set theseto be α = 300 and σ = 20, based on the resulting patchesappearance. After this, the stress field is applied to the image,the breast segmentation mask and mass annotations. This isdone by moving each pixel to a new position (eq. (3)) andusing spline interpolation of order one to obtain intensitiesat integer coordinates. An example of the effects of suchdeformation is show in Figure 3.

∆x = G(σ) ∗ (α×Rand(n,m)) (1)∆y = G(σ) ∗ (α×Rand(n,m)) (2)

Itrans(j+∆x(j, k), k + ∆y(j, k)) = I(j, k) (3)

In the equations above, I and Itrans are the original andtransformed images, respectively; and n ×m are the mam-mogram dimensions.

C. End-to-end mass detection

In this section, we briefly sketch the proposed methodend-to-end. From training (on patches) to inference (on fullmammograms).

A network similar to the one shown in Figure 2 is trainedusing patches of masses and normal breast tissue. Theseare extracted as described in the beginning of Section II.Balanced batches of positive and negative images are fed tothe classifier. Due to the existing imbalance, the model willrepeat positive cases much more frequently than negativeones. We use data augmentation on the positive class to makeits samples different from the originals.

During inference: (1) by transforming the trained net-work into a FCN, we obtain, for each test mammogram,a probability map that indicates a prediction of whethera lesion is present in each area of the exam image; (2)the resulting probability map is thresholded, with a value(≈ 0.5) depending on the dataset; (3) from the resultingbinary image, small objects are removed via morphologicalopening; and finally (4) predicted lesion detections are theregions that survive the previous step. Bounding boxes areobtained for each region, and are evaluated against ground-truth annotations.

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III. EXPERIMENTS

There are two sets of experiments. First, using the pro-posed CNN architecture we compare two strategies for dataaugmentation: traditional vs. elastic deformations. For this,40 transformations of each image are computed before train-ing. Second, we compare the performance of our proposedCNN architecture against state-of-the-art methods.A. Datasets

We make use of three publicly available datasets summa-rized in Table I.

INbreast [23] is composed of high quality full-field digital(FFD) mammograms of both healthy and unhealthy patientsas well as detailed lesion annotations. Because INbreast doesnot a have a standard train/test split, we use stratified five-fold cross validation with a proportion of 80/20% (train/test)for a more robust measure of performance.

CBIS [24] is a Curated Breast Image Subset ofDDSM [25], provided by The Cancer Imaging Archive [26]divided in a fixed train/test split. In particular: questionablecases were removed, images were standardized to the DI-COM format, and lesion annotation was improved.

BCRP [25] is a fixed split (train/test) of the most chal-lenging cases from DDSM [25].

Important to note that in the case of CBIS and BCRP,images were obtained by digitizing mammograms that wereoriginally on film. This results in lower quality samples whencompared to the FFD mammograms of INbreast. Both BCRPand CBIS are divided into masses and calcifications. We onlyuse the former set of images.

TABLE I: Dataset summary used in the experiments.

Cases Images Masses

train test train test train test

INbreast 108 410 116

CBIS 691 201 1231 361 1318 378

BCRP 39 40 156 160 84 87

B. Detection and Evaluation

At inference time, the full image (mammogram) is for-ward propagated through the FCN to obtain a probabilitymap which is then thresholded and filtered. Isolated blobsare counted as detections. At this stage there is no dataaugmentation. Following common practice, the true positive(TP) criterion is met when the intersection over union (IoU)of the mass’s bounding box and prediction bounding box isgreater then 0.2. Region-based analysis is done by means ofthe Free Response Operating Characteristic (FROC) curve.This plots the true positive rate (TPR, or sensitivity) as afunction of the number of false positives per image (FPI).The curves for the two data augmentation strategies for CBISand BCRP are shown in Figure 4.

C. Results

FROC curves are summarized in Table II for TPR levelsof 80% or 60% depending on the dataset. In the case ofthe BCRP, a more challenging dataset, a threshold of 0.6

Fig. 4: FROC curve, showing sensitivity vs. number of false-positives per image. Top - CBIS; Bottom - BCRP

was required to avoid multiple detections being connectedin the thresholded image and thus considered as a singleone. We also used a TPR of 60%, as a TPR of 80% is stillnot attainable by any CAD system that we are aware of.Comparison between our elastic deformation strategy and atraditional data augmentation method can also be seen inFigure 4 for different levels of FPI.

TABLE II: Number of false-positives per image (FPI) mea-sured at 80% sensitivity (TPR) for “INbreast” and “CBIS”,and at 60% for the more challenging “BCRP”.

INbreast [23] CBIS [24] BCRP [25]

TPR FPI TPR FPI TPR FPI

elastic 0.8 1.171 0.8 3.509 0.6 1.864benchmark 0.8 0.912 0.8 5.757 0.6 3.047

thres. 0.5 0.5 0.6

Data augmentation: even-though the strategy based onelastic deformations is not a winner across-the-board, itis worth noting that in the cases where it does performbetter – CBIS and BCRP datasets –, for the same level ofsensitivity the number of FPI drops ≈ 40% when comparedto FPI achieved by traditional data augmentation (i.e. denoted“benchmark” in Table II).

CNN architecture: When used together with the elasticdeformation strategy for data augmentation, the proposedCNN compares competitively with other known methods.Table III summarizes the best reported results for the publicdatasets used in these experiments. In particular, for the IN-

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breast dataset, the recent work of Dhungel et al. [12] achievesimpressive sensitivity (0.96± 0.03) values for a comparablenumber of FPI. We note however their framework is basedon a much more complex pipeline that includes deep-beliefnetworks, Gaussian mixture models, a cascade of R-CNNand a cascade of random forests. When compared to moretraditional methods [27], [28] we see that our deep learningapproach presents much less FP per image. However, a TPRof 0.7 was not achieved in the BCRP dataset.

TABLE III: Comparison to other methods, including knownstate-of-the-art for benchmark datasets.

INbreast [23] CBIS [24] BCRP [25]

TPR FPI TPR FPI TPR FPI

[12]0.96 ±0.03 1.2

-0.75 4.8

0.87 ±0.14 0.8 0.70 4.0

[27] 0.8 2.5 - -

[28] - - 0.70 8.0

elastic 0.8 1.171 0.8 3.509 0.6 1.864

IV. CONCLUSIONSDuring a real-life screening, different views of the same

breast can be obtained from the application of differentcompression forces. This however should not change theoutcome of screening. In this paper we aim at augmenting thetraining data by simulating this phenomena. The extensiveexperimental results using elastic deformations show thatthis data augmentation technique can be used to improveperformance of CNN models in mass detection. Anotherstrategy that we are currently studying, is to perform elasticdeformations at the patch level. Perhaps less intuitive, thisstrategy does have the potential to generate masses with afiner-level of detail. Additionally, other types of stretchingcould be considered.

V. ACKNOWLEDGMENTSThis work was funded by project NanoSTIMA, Macro-

to-Nano Human Sensing: Towards Integrated MultimodalHealth Monitoring and Analytics, NORTE-01-0145-FEDER-000016. Project funded by North Portugal Regional Opera-tional Programme (NORTE 2020), under PORTUGAL 2020Partnership Agreement, and through the European RegionalDevelopment Fund (ERDF).

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